Example: Solve the equation .

First we check that this is indeed an exact equation and then we show how to find .

> M:=(x,y)->1-sin(x)*tan(y);N:=(x,y)->cos(x)/(cos(y))^2;

Here Ex stands for exact.

> diff(M(x,y),y)-diff(N(x,y),x);

> simplify(%);

Since the difference is , we see that the equation is an exact differential equation. Next, we find by using the following formula

> Ex;

> simplify(%,trig);

> f:=unapply(Ex,(x,y));